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Title: A strong completeness theorem for the gentzen systems associated with finite algebras
Author: Gil, Àngel J.
Rebagliato, Jordi
Verdú, B. (Buenaventura)
Keywords: Lògica matemàtica
Teoria de la prova
Universitat de Barcelona. Institut de Matemàtica
Issue Date: 1996
Publisher: Universitat de Barcelona
Series/Report no: Mathematics Preprint Series; 218
Abstract: In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems.
Note: Preprint enviat per a la seva publicació en una revista científica: Journal of Applied Non-Classical Logics. 1999, vol. 9, issue 1, pp 9-36. []
Note: Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 37.13]
Appears in Collections:Preprints de Matemàtiques - Mathematics Preprint Series

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